For finding the $n$th prime (or the number of primes less than a number), there are results for large numbers; I was wondering if something similar for the totatives of a primorial number is possible (where a totative is a number less than $n$ and coprime with $n$)(i.e. given a similarly large primorial number, find the $n$th totative of the primorial or find the number of totatives of a primorial number that are less than $n$). I am thinking of numbers with size of $10^{20}$ since that is possible for the $n$th prime algorithms.
Note: The primorial $p_k$# is defined as the product of the first $k$ primes (in mathematical notation, this can be written as $p_k$# $= \prod_{r=1}^{n}p_k$).